F₁-ATPase, the sector of ATP synthase where the synthesis of cellular ATP occurs, is a rotary molecular motor in its own right. Driven by ATP hydrolysis, direct observation of the rotation of the central axis within single molecules of F₁ is possible. Operating at close to 100% efficiency, F₁ from thermophilic Bacillus has been shown to produce ~40pN˙nm of torque during rotation. This thesis details the groundwork required for the direct measurement of the torque produced by F₁ using a rotary angle clamp, an optical trapping system specifically designed for application to rotary molecular motors. Proof-of-concept experiments will be presented thereby demonstrating the ability to directly manipulate single F₁ molecules from Escherichia coli and yeast mitochondria (Saccharomyces cerevisiae), along with activation of F₁ out of its inhibited state by the application of external torque. Despite in-depth knowledge of the rotary mechanism of F₁ from thermophilic Bacillus, the rotation of F₁ from Escherichia coli is relatively poorly understood. A detailed mechanical characterization of E.coli F₁ will be presented here, with particular attention to the ground states within the catalytic cycle, notably the ATP-binding state, the catalytic state and the inhibited state. The fundamental mechanism of E.coli F₁ appears to depart little from that of F₁ from thermophilic Bacillus, although, at room temperature, chemical processes occur faster within the E.coli enzyme, in line with considerations regarding the physiological conditions of the different species. Also presented here is the verification of the rotary nature of yeast mitochondrial F₁. The torque produced by F₁ from thermophilic Bacillus, E.coli and yeast mitochondria is the same, within experimental error, despite their diverse evolutionary and environmental origins.